%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:10:11 PM UTC 2026
% Result : Theorem 0.02s 0.32s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 80 ( 8 unt; 5 def)
% Number of atoms : 240 ( 57 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 265 ( 105 ~; 114 |; 31 &)
% ( 13 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 106 ( 98 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C] :
( union(B,C) = empty_set
<=> ( C = empty_set
& B = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C] :
( union(B,C) = empty_set
<=> ( C = empty_set
& B = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [B,C,D] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
( ! [B,C,D] :
( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ! [B,C,D] :
( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f18,plain,
( ! [B,C] :
( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f23,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [B,C] :
( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f26,plain,
( ! [B,C] :
( ( ~ member(sK0_skl(C,B),C)
& member(sK0_skl(C,B),B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f25]) ).
fof(f27,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f36,plain,
! [B,C] :
( ( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ( ! [D] :
( ( ~ member(D,C)
| member(D,B) )
& ( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f37,plain,
( ! [B,C] :
( ? [D] :
( ( member(D,C)
| member(D,B) )
& ( ~ member(D,C)
| ~ member(D,B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f38,plain,
( ! [B,C] :
( ( ( member(sK2_skl(C,B),C)
| member(sK2_skl(C,B),B) )
& ( ~ member(sK2_skl(C,B),C)
| ~ member(sK2_skl(C,B),B) ) )
| B = C )
& ! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| member(D,B) )
& ! [D] :
( member(D,C)
| ~ member(D,B) ) )
| B != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(D,sK2_skl(C,B))],[f37]) ).
fof(f42,plain,
! [X0,X1] :
( member(sK2_skl(X1,X0),X1)
| member(sK2_skl(X1,X0),X0)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f43,plain,
? [B,C] :
( union(B,C) = empty_set
<~> ( C = empty_set
& B = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f44,plain,
? [B,C] :
( ( C != empty_set
| B != empty_set
| union(B,C) != empty_set )
& ( ( C = empty_set
& B = empty_set )
| union(B,C) = empty_set ) ),
inference(NNF_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
( ( sK4_skl != empty_set
| sK3_skl != empty_set
| union(sK3_skl,sK4_skl) != empty_set )
& ( ( sK4_skl = empty_set
& sK3_skl = empty_set )
| union(sK3_skl,sK4_skl) = empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f44]) ).
fof(f46,plain,
( sK3_skl = empty_set
| union(sK3_skl,sK4_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
( sK4_skl = empty_set
| union(sK3_skl,sK4_skl) = empty_set ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f48,plain,
( sK4_skl != empty_set
| sK3_skl != empty_set
| union(sK3_skl,sK4_skl) != empty_set ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f49,definition,
( sQ0_spl
<=> union(sK3_skl,sK4_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ0_spl
| union(sK3_skl,sK4_skl) = empty_set ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f51,plain,
( sQ0_spl
| union(sK3_skl,sK4_skl) != empty_set ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,definition,
( sQ1_spl
<=> sK3_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ1_spl
| sK3_skl = empty_set ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f54,plain,
( sQ1_spl
| sK3_skl != empty_set ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f49,f52]) ).
fof(f56,definition,
( sQ2_spl
<=> sK4_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ2_spl
| sK4_skl = empty_set ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f58,plain,
( sQ2_spl
| sK4_skl != empty_set ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f49,f56]) ).
fof(f60,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f49,f52,f56]) ).
fof(f61,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f19]) ).
fof(f67,plain,
! [X0] :
( ~ sQ0_spl
| ~ member(X0,sK3_skl)
| member(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f50,f14]) ).
fof(f70,plain,
! [X0] :
( ~ sQ0_spl
| ~ member(X0,sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f67,f16]) ).
fof(f71,plain,
! [X0] :
( ~ sQ0_spl
| ~ member(X0,sK4_skl)
| member(X0,empty_set) ),
inference(paramodulation,[status(thm)],[f50,f15]) ).
fof(f74,plain,
! [X0] :
( ~ sQ0_spl
| ~ member(X0,sK4_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f16]) ).
fof(f75,plain,
( sQ1_spl
| ~ subset(empty_set,sK3_skl)
| ~ subset(sK3_skl,empty_set) ),
inference(resolution,[status(thm)],[f21,f54]) ).
fof(f77,definition,
( sQ3_spl
<=> subset(sK3_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( sQ3_spl
| ~ subset(sK3_skl,empty_set) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,definition,
( sQ4_spl
<=> subset(empty_set,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( sQ4_spl
| ~ subset(empty_set,sK3_skl) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,plain,
( sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f75,f77,f80,f52]) ).
fof(f87,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ subset(X0,empty_set) ),
inference(resolution,[status(thm)],[f27,f16]) ).
fof(f90,plain,
! [X0,X1] :
( member(X0,X1)
| ~ member(X0,union(empty_set,X1)) ),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f94,plain,
! [X0] :
( ~ sQ0_spl
| subset(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f28,f74]) ).
fof(f95,plain,
! [X0] :
( ~ sQ0_spl
| subset(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f28,f70]) ).
fof(f96,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f28,f16]) ).
fof(f97,plain,
( sQ3_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f79,f95]) ).
fof(f98,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f97]) ).
fof(f99,plain,
( sQ0_spl
| ~ sQ1_spl
| union(empty_set,sK4_skl) != empty_set ),
inference(forward_demodulation,[status(thm)],[f53,f51]) ).
fof(f100,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| union(empty_set,empty_set) != empty_set ),
inference(backward_demodulation,[status(thm)],[f57,f99]) ).
fof(f101,plain,
! [X0] :
( member(sK2_skl(X0,empty_set),X0)
| empty_set = X0 ),
inference(resolution,[status(thm)],[f42,f16]) ).
fof(f113,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f96]) ).
fof(f114,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f113]) ).
fof(f117,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ subset(empty_set,empty_set) ),
inference(backward_demodulation,[status(thm)],[f53,f79]) ).
fof(f119,plain,
( sQ3_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f61]) ).
fof(f120,plain,
( sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f119]) ).
fof(f130,plain,
! [X0] :
( empty_set = X0
| ~ subset(X0,empty_set) ),
inference(resolution,[status(thm)],[f87,f101]) ).
fof(f140,plain,
! [X0] : ~ member(X0,union(empty_set,empty_set)),
inference(resolution,[status(thm)],[f90,f16]) ).
fof(f181,plain,
empty_set = union(empty_set,empty_set),
inference(resolution,[status(thm)],[f140,f101]) ).
fof(f193,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f181,f100]) ).
fof(f194,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f193]) ).
fof(f214,plain,
( sQ2_spl
| ~ subset(sK4_skl,empty_set) ),
inference(resolution,[status(thm)],[f58,f130]) ).
fof(f223,plain,
( sQ2_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f214,f94]) ).
fof(f224,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f223]) ).
fof(f225,plain,
$false,
inference(sat_refutation,[status(thm)],[f55,f59,f60,f83,f98,f114,f120,f194,f224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Mon Sep 21 05:28:06 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 0.02/0.32 % Refutation found
% 0.02/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.02/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.34 % Elapsed time: 0.041689 seconds
% 0.02/0.34 % CPU time: 0.114831 seconds
% 0.02/0.34 % Total memory used: 48.520 MB
% 0.02/0.34 % Net memory used: 48.253 MB
%------------------------------------------------------------------------------